Ms Slungile Tshibase’s dissertation for her Master’s in Applied Mathematics tackled λ(Lambda)-Symmetries – specifically symmetries that could help analyse and simplify complex equations where traditional methods fail.
Supervised by Professor Kesh Govinder, Tshibase’s research – which rewarded her with a cum laude result – was completed in a year and involved the λ-symmetries developed in 2001 that expanded on classical Lie point symmetries, presenting an improved method to study differential equations, particularly those without classical symmetries.
Tshibase’s work unearthed a surprising result about the Painlevé-Ince equation, a well-known type of nonlinear differential equation, in that certain λ-symmetries can simplify the Painlevé-Ince equation, leading to new methods for analysing its solutions and understanding its behaviour in various situations.
Originally from uMzimkhulu, her academic journey began at Sehole Combined School in Harding, which nurtured her love for learning, particularly mathematics and science. Tshibase found working with numbers and solving problems deeply satisfying, later learning that her late mother also loved mathematics.
Tshibase aimed to pursue tertiary studies and was initially accepted for studies in Accounting at UKZN in Pietermaritzburg, realising during registration that mathematics was a better fit, and moving to the College of Agriculture, Engineering and Science (CAES) on the Westville campus.
Despite the overwhelming programme, Tshibase found her niche in the discipline and majored in Applied Mathematics and Statistics, with her honours and master’s degrees in Applied Mathematics.
Tshibase found that UKZN offered everything a student would need discovering its many resources.
Completing her master’s degree in a year was a challenge, but the support of Govinder and the CAES helped Tshibase manage the pressure of her studies, keeping her on a tight schedule and helping her focus on her objectives.
During her studies, Tshibase also tutored undergraduate Mathematics students and worked as a tutor for the Rotary Club of Durban Umhlatuzana. Staying organised, prioritising tasks and managing her time well helped Tshibase balance her personal life and academic responsibilities.
Tshibase has now progressed to PhD studies and is continuing her research on λ-symmetries, building on her honours and master’s projects. She is excited to contribute more to the field and is considering crafting a career in academia thanks to her enjoyment of research, continuous learning and sharing her knowledge through teaching. She is also exploring opportunities in industry or research organisations as she gains experience through her PhD programme and expands her network.
Tshibase thanked Govinder for his guidance, motivation and support, which provided a constant source of strength and helped her secure funding. He ensured she persevered through challenging times and supported her as she developed her academic skills.
She also thanked UKZN for the opportunities it provided for academic growth as well as her family and friends for their unwavering support, encouragement and faith in her, saying their love and presence kept her grounded.
Tshibase acknowledged the National Student Financial Aid Scheme (NSFAS), the National Research Foundation (NRF), the Department of Science, Technology and Innovation-NRF Centre of Excellence in Mathematical and Statistical Science, and UKZN for supporting her studies financially.
Words: Christine Cuénod
Photograph: Sethu Dlamini
